JMSJ 論文賞受賞者のことば
JMSJ とは、日本数学会の出版する学術雑誌 Journal of the MathematicalSociety of Japan の略称です．JMSJ 論文賞(The JMSJ Outstanding Paper Prize)
は，授賞年前年の JMSJ に掲載された論文のうち特に優れたもの（3 篇以内）の著者に贈られる賞です．2017 年 JMSJ 論文賞は以下の 1 篇に贈られました．
著者：Bo Berndtsson 氏 (Chalmers University of Technology)，László Lempert氏 (Purdue University)
論文題目： A proof of the Ohsawa—Takegoshi theorem with sharp estimates,
JMSJ, 68(2016), 1461-1472.
受賞者のことば：We both are delighted and honored to have received the Outstanding PaperPrize. It adds to our happiness that this distinction comes from the Japanese
Mathematical Society, because for over eighty years now Japanese mathematics
has played a special role in our larger subject, complex analysis and geometry.
Our paperthat the Society judged worthy has also been directly inspired by Japanesemathematics, an amazing theorem that Ohsawa and Takegoshi found in the1980s, a result that has not ceased to fascinate complex analysts ever since. For
this reason, and because perhaps not all readers of Sugaku Tushin are familiar
with this story, we hope that in this acknowledgement we will be permitted toreview at least a few instances of the decisive role that Japanese mathematicians
have played in the development of complex analysis and geometry.
The beginnings of the story go back to the 1930s. By then Behnke and Thullenin Germany have clearly delineated the central problems of the young subject ofcomplex analysis of several variables; but nobody had any idea how to attack
those problems. Nobody, that is, except Oka. Oka as a young man in his thirties
not only realized the importance of the problems, but devised a program to solve
them. It took him some fifteen years to accomplish his program. More than that,right from the beginning he had an unparalleled vision that the solutions of theproblems would surpass the boundaries of complex analysis of several variables,
and will be significant for other areas within mathematics. History proved him
right. He planted the seeds of the theory of coherent sheaves, without which
fields such as contemporary algebraic geometry or number theory would beunimaginable.

In the 1940s—50s it was Kodaira's turn to revolutionize complex analysis andgeometry. He took up certain heuristic ideas in algebraic geometry that Hodge
had proposed in the 1930s, put them on firm footing, and exploited their fullpotential. The results he obtained were stunning. He showed that the global
theory of systems of elliptic partial differential equations of second order－that
he himself developed－is a powerful tool in the study of compact complex
manifolds, in particular of projective algebraic manifolds. In analogy with
Bochner's work in Riemannian geometry, he demonstrated how curvature can beplayed out to prove that certain differential equations relevant to complex
analysis are solvable: in other words, that certain cohomology groups vanish. The
identities of Kodaira, Akizuki, and Nakano are still the cornerstones of thevanishing theorems in complex analysis and geometry.
In our research we have been deeply influenced by the works and insights ofOka, Kodaira, Akizuki, and Nakano, but also, as said before, of their successors,
Ohsawa and Takegoshi among others. It is clear none of this would have beenpossible without the commitment of the broader Japanese society to value
intellectual. We greatly admire this, and see the prizes of the Japanese
Mathematical Society－ours, and other prizes－as a sign thereof.
Thanks to the Society again,
B.B. and L.L.